Please help! How to calculate this? PP$2)$ Flow across banks of tubes $($Incropera ch$.7\mathrm{.}6,$ Flow Across Banks of Tubes$)$ Consider a bank of tubes in a staggered arrangement. The tube diameter is D $=1\mathrm{.}5$ cm$,$ the transverse pitch is ST $=3$ cm and the longitudinal pitch is SL $=3\mathrm{.}5$ cm$.$ See Figure $1$ for reference. The air flows at a velocity of V $=6$ m$/$s and is initially at a temperature of Ti $=20$C$.$ The tubes are at a temperature of Ts $=100$C and the air is to be heated at To $=70$C$.$ How many rows of tubes are needed? Find fluid properties from the literature. The thermodynamic properties of air are evaluated at the arithmetic mean of the inlet and outlet temperatures T $=($Ti $+$ To$)/2=318$K $($ $=1\mathrm{.}11$kg$/$m$3,$ $=1\mathrm{.}74$x$105$m$2/$s$,$ k $=0\mathrm{.}02772$W$/$mK$,$ cp $=1007$J$/$kgK$,$ P r $=0\mathrm{.}7016)$ Air properties at the surface temperature are: $($ $=0\mathrm{.}947$kg$/$m$3,$ $=2\mathrm{.}297$x$105$m$2/$s$,$ k $=0\mathrm{.}03162$W$/$mK$,$ cp $=1011$J$/$kgK$,$ P r $=0\mathrm{.}6955)$ For the Nusselt number, you may use the following correlation: NuD $=$ C$1$Rem D$,$maxP r$0\mathrm{.}36$ P r P rs $1/4(1)$ where C$1,$ and m are found in the tables in Figure $2,$ and P rs is the Prandtl number of air at the surface temperature.

Here is some tips: The energy balance for the system is: q $=$ mcp$($To $$ Ti$)=$ hAs$$Tlm Surface area to calculate the mass flow and the area of $$the pipes depends on the control volume $($control volume$)$ selection. The Reynolds number is calculated for the maximum speed according to which is the speed in the narrowest gap between the pipes. The characteristic length is the pipe diameter for Reynolds and Nusselt numbers. The correlation for the Nusselt number is: NuD $=$ C$1$Rem D$,$maxP r$0\mathrm{.}36$ p r P rs $14$ The values $$C$1$ and m can be obtained from the table in the task handout. To define the control volume, think about the symmetry of the system. Hint: The length of the pipes or the measure of the pipes in the y$-$direction does not affect the pipe rows I measure. The correct answer is about N $=30$ lines. Kuva $1$: A schematic of a bank of tubes in a staggered arrangement.

Kuva $2$: Constants used in the correlation for the Nusselt number.